arXiv subjects

Kenta Kasai

Publications and source records attributed to Kenta Kasai.

At least 55 records · Page 3Linked to original sources

arXiv2013

Efficient Termination of Spatially-Coupled Codes

Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear equations to terminate the encoding process. In this paper, we propose modified spatially-coupled codes. The modified $(\dl,\dr,L)$ codes have less rate-loss, i.e., higher coding rate, and have the same threshold as $(\dl,\dr,L)$ codes and are efficiently terminable by using an accumulator.

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arXiv2013

Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.

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arXiv2012

Approaching the Capacity of Large-Scale MIMO Systems via Non-Binary LDPC Codes

In this paper, the application of non-binary low-density parity-check (NBLDPC) codes to MIMO systems which employ hundreds of antennas at both the transmitter and the receiver has been proposed. Together with the well-known low-complexity MMSE detection, the moderate length NBLDPC codes can operate closer to the MIMO capacity, e.g., capacity-gap about 3.5 dB (the best known gap is more than 7 dB). To further reduce the complexity of MMSE detection, a novel soft output detection that can provide an excellent coded performance in low SNR region with 99% complexity reduction is also proposed. The asymptotic performance is analysed by using the Monte Carlo density evolution. It is found that the NBLDPC codes can operate within 1.6 dB from the MIMO capacity. Furthermore, the merit of using the NBLDPC codes in large MIMO systems with the presence of imperfect channel estimation and spatial fading correlation which are both the realistic scenarios for large MIMO systems is also pointed out.

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arXiv2012

Spatially-Coupled Binary MacKay-Neal Codes for Channels with Non-Binary Inputs and Affine Subspace Outputs

We study LDPC codes for the channel with $2^m$-ary input $\underline{x}\in \mathbb{F}_2^m$ and output $\underline{y}=\underline{x}+\underline{z}\in \mathbb{F}_2^m$. The receiver knows a subspace $V\subset \mathbb{F}_2^m$ from which $\underline{z}=\underline{y}-\underline{x}$ is uniformly chosen. Or equivalently, the receiver receives an affine subspace $\underline{y}-V$ where $\underline{x}$ lies. We consider a joint iterative decoder involving the channel detector and the LDPC decoder. The decoding system considered in this paper can be viewed as a simplified model of the joint iterative decoder over non-binary modulated signal inputs e.g., $2^m$-QAM. We evaluate the performance of binary spatially-coupled MacKay-Neal codes by density evolution. The iterative decoding threshold is seriously degraded by increasing $m$. EXIT-like function curve calculations reveal that this degradation is caused by wiggles and can be mitigated by increasing the randomized window size. The resultant iterative decoding threshold values are very close to the Shannon limit.

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arXiv2012

Ultra Low Complexity Soft Output Detector for Non-Binary LDPC Coded Large MIMO Systems

The theoretic results of MIMO capacity tell us that the higher the number of antennas are employed, the higher the transmission rate is. This makes MIMO systems with hundreds of antennas very attractive but one of the major problems that obstructs such large dimensional MIMO systems from the practical realization is a high complexity of the MIMO detector. We present in this paper the new soft output MIMO detector based on matched filtering that can be applied to the large MIMO systems which are coded by the powerful non-binary LDPC codes. The per-bit complexity of the proposed detector is just 0.28% to that of low complexity soft output MMSE detector and scales only linearly with a number of antennas. Furthermore, the coded performances with small information length 800 bits are within 4.2 dB from the associated MIMO capacity.

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arXiv2012

Near Capacity Approaching for Large MIMO Systems by Non-Binary LDPC Codes with MMSE Detection

In this paper, we have investigated the application of non-binary LDPC codes to spatial multiplexing MIMO systems with a large number of low power antennas. We demonstrate that such large MIMO systems incorporating with low-complexity MMSE detector and non-binary LDPC codes can achieve low probability of bit error at near MIMO capacity. The new proposed non-binary LDPC coded system also performs better than other coded large MIMO systems known in the present literature. For instance, non-binary LDPC coded BPSK-MIMO system with 600 transmit/receive antennas performs within 3.4 dB from the capacity while the best known turbo coded system operates about 9.4 dB away from the capacity. Based on the simulation results provided in this paper, the proposed non-binary LDPC coded large MIMO system is capable of supporting ultra high spectral efficiency at low bit error rate.

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arXiv2011

Simple Low-Rate Non-Binary LDPC Coding for Relay Channels

Binary LDPC coded relay systems have been well studied previously with the assumption of infinite codeword length. In this paper, we deal with non-binary LDPC codes which can outperform their binary counterpart especially for practical codeword length. We utilize non-binary LDPC codes and recently invented non-binary coding techniques known as multiplicative repetition to design the low-rate coding strategy for the decode-and-forward half-duplex relay channel. We claim that the proposed strategy is simple since the destination and the relay can decode with almost the same computational complexity by sharing the same structure of decoder. Numerical experiments are carried out to show that the performances obtained by non-binary LDPC coded relay systems surpass the capacity of direct transmission and also approach within less than 1.5 dB from the achievable rate of the relay channels.

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arXiv2011

Threshold Improvement of Low-Density Lattice Codes via Spatial Coupling

Spatially-coupled low-density lattice codes (LDLC) are constructed using protographs. Using Monte Carlo density evolution using single-Gaussian messages, we observe that the threshold of the spatially-coupled LDLC is within 0.22 dB of capacity of the unconstrained power channel. This is in contrast with a 0.5 dB noise threshold for the conventional LDLC lattice construction.

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arXiv2011

Multiplicatively Repeated Non-Binary LDPC Codes

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform the best low-rate binary LDPC codes so far. Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.

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arXiv2011

Quantum Error Correction beyond the Bounded Distance Decoding Limit

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.

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arXiv2011

Spatially Coupled LDPC Codes for Decode-and-Forward in Erasure Relay Channel

We consider spatially-coupled protograph-based LDPC codes for the three terminal erasure relay channel. It is observed that BP threshold value, the maximal erasure probability of the channel for which decoding error probability converges to zero, of spatially-coupled codes, in particular spatially-coupled MacKay-Neal code, is close to the theoretical limit for the relay channel. Empirical results suggest that spatially-coupled protograph-based LDPC codes have great potential to achieve theoretical limit of a general relay channel.

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arXiv2011

Design and Performance of Rate-compatible Non-Binary LDPC Convolutional Codes

In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felstroem and Zigangirov construction for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-regular non-binary LDPC convolutional code of rate 1/2. Higher-rate codes are produced by puncturing the mother code and lower-rate codes are produced by multiplicatively repeating the mother code. Simulation results show that non-binary LDPC convolutional codes of rate 1/2 outperform state-of-the-art binary LDPC convolutional codes with comparable constraint bit length. Also the derived low-rate and high-rate non-binary LDPC convolutional codes exhibit good decoding performance without loss of large gap to the Shannon limits.

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arXiv2011

Analytical Solution of Covariance Evolution for Irregular LDPC Codes

A scaling law developed by Amraoui et al. is a powerful technique to estimate the block error probability of finite length low-density parity-check (LDPC) codes. Solving a system of differential equations called covariance evolution is a method to obtain the scaling parameter. However, the covariance evolution has not been analytically solved. In this paper, we present the analytical solution of the covariance evolution for irregular LDPC code ensembles.

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arXiv2011

Analysis of Error Floors of Non-Binary LDPC Codes over MBIOS Channel

In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the belief propagation decoder. We consider an expurgated ensemble of non-binary LDPC codes by using the above necessary and sufficient condition, and hence exhibit lower error floors. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channel.

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arXiv2011

Spatially Coupled Quasi-Cyclic Quantum LDPC Codes

We face the following dilemma for designing low-density parity-check codes (LDPC) for quantum error correction. 1) The row weights of parity-check should be large: The minimum distances are bounded above by the minimum row weights of parity-check matrices of constituent classical codes. Small minimum distance tends to result in poor decoding performance at the error-floor region. 2) The row weights of parity-check matrices should not be large: The sum-product decoding performance at the water-fall region is degraded as the row weight increases. Recently, Kudekar et al. showed spatially-coupled (SC) LDPC codes exhibit capacity-achieving performance for classical channels. SC LDPC codes have both large row weight and capacity-achieving error-floor and water-fall performance. In this paper, we design SC LDPC-CSS (Calderbank, Shor and Steane) codes for quantum error correction over the depolarizing channels.

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arXiv2011

Spatially Coupled Codes over the Multiple Access Channel

We consider spatially coupled code ensembles over a multiple access channel. Convolutional LDPC ensembles are one instance of spatially coupled codes. It was shown recently that, for transmission over the binary erasure channel, this coupling of individual code ensembles has the effect of increasing the belief propagation threshold of the coupled ensembles to the maximum a-posteriori threshold of the underlying ensemble. In this sense, spatially coupled codes were shown to be capacity achieving. It was observed, empirically, that these codes are universal in the sense that they achieve performance close to the Shannon threshold for any general binary-input memoryless symmetric channels. In this work we provide further evidence of the threshold saturation phenomena when transmitting over a class of multiple access channel. We show, by density evolution analysis and EXIT curves, that the belief propagation threshold of the coupled ensembles is very close to the ultimate Shannon limit.

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arXiv2011

Threshold Saturation on Channels with Memory via Spatial Coupling

We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the memoryless binary erasure channel, this coupling increases the belief propagation threshold of the ensemble to the maximum a-posteriori threshold of the underlying component ensemble. This paved the way for a new class of capacity achieving low-density parity check codes. It was also shown empirically that the same threshold saturation occurs when we consider transmission over general binary input memoryless channels. In this work, we report on empirical evidence which suggests that the same phenomenon also occurs when transmission takes place over a class of channels with memory. This is confirmed both by simulations as well as by computing EXIT curves.

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arXiv2010

Effects of Single-Cycle Structure on Iterative Decoding for Low-Density Parity-Check Codes

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) codes and belief propagation (BP) decoding. For fixed numbers of BP iterations, the bit error probability approaches a limit as blocklength tends to infinity, and the limit is obtained via density evolution. On the other hand, the difference between the bit error probability of codes with blocklength $n$ and that in the large blocklength limit is asymptotically $α(ε,t)/n + Θ(n^{-2})$ where $α(ε,t)$ denotes a specific constant determined by the code ensemble considered, the number $t$ of iterations, and the erasure probability $ε$ of the BEC. In this paper, we derive a set of recursive formulas which allows evaluation of the constant $α(ε,t)$ for standard irregular ensembles. The dominant difference $α(ε,t)/n$ can be considered as effects of cycle-free and single-cycle structures of local graphs. Furthermore, it is confirmed via numerical simulations that estimation of the bit error probability using $α(ε,t)$ is accurate even for small blocklengths.

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